To add to Rebekah's excellent post-- yes, when DD was so sensitive and little, most of her allergens simply weren't in the house at all. The reason for this was/is twofold: number one, it was my own selfish need to have SOMEWHERE that I could let down my guard just a little-- the years from 0 to five probably took two decades off of my own life, I swear-- and secondly, I wanted a place that was safe enough that I could allow DD some normal developmental space. EVERYTHING else, EVERYWHERE else, I was constantly snatching her up and away from dangers. It was crazy-making. I had to have a place where I knew the risk was minimal, where I could allow her to play just out of sight, and roam around touching/mouthing things like a normal toddler.
I still recall a friend stating to me when my DD was nearly three and I'd just slapped a hand and snatched her up into my arms that "you can't stop them from picking things up off the ground-- it's a developmental thing" and then she and I just stared at one another, and she realized that my choices were pretty bleak, there-- normal development or a living child. I chose the latter, obviously, but it was at the cost of some normal developmental exploration. At least in an allergen-free home, they can still be toddlers.
Anything that has triggered anaphylaxis from cross-contamination, (for any member of the household) is an off-limits thing in the house. That's just sort of our house policy, though. We do occasionally bring in allergens for direct consumption, though-- for example, I will sometimes have a sandwich that has mayo on it. But I'm VERY careful, and I didn't even do that back when DD was still so allergic to egg that she couldn't do things made on shared lines at all. When DD outgrew her wheat allergy, I can still remember buying a bag of flour, which was something I hadn't done in four years.
Our house is now peanut, walnut, pistachio, cashew, and shellfish free. We're not entirely soy free, nor milk-free, nor egg-free (anymore). But there are still some things that some household members can't/don't eat, and we're careful.